Learning agent behaviors from observational data has shown to improve our understanding of their decision-making processes, advancing our ability to explain their interactions with the environment and other agents. While multiple learning techniques have been proposed in the literature, there is one particular setting that has not been explored yet: multi agent systems where agent identities remain anonymous. For instance, in financial markets labeled data that identifies market participant strategies is typically proprietary, and only the anonymous state-action pairs that result from the interaction of multiple market participants are publicly available. As a result, sequences of agent actions are not observable, restricting the applicability of existing work. In this paper, we propose a Policy Clustering algorithm, called K-SHAP, that learns to group anonymous state-action pairs according to the agent policies. We frame the problem as an Imitation Learning (IL) task, and we learn a world-policy able to mimic all the agent behaviors upon different environmental states. We leverage the world-policy to explain each anonymous observation through an additive feature attribution method called SHAP (SHapley Additive exPlanations). Finally, by clustering the explanations we show that we are able to identify different agent policies and group observations accordingly. We evaluate our approach on simulated synthetic market data and a real-world financial dataset. We show that our proposal significantly and consistently outperforms the existing methods, identifying different agent strategies.

LOBs [22] are a fundamental market mechanism, which are used across a significant proportion of financial markets, including all major stock and derivatives exchanges. The benefits of having robust and realistic simulators for these markets are numerous. For example, they would allow the study of markets under different assumptions, and the investigation of AI techniques for training trading strategies. In a LOB market, matched orders result in trades and unmatched orders are stored in the two parts of the LOB, a collection of buy orders called bids (the bid book), and a collection of sell orders called asks (the ask book). Typically, each side of the LOB will contains hundreds of individual orders, and a real market would be updated at micro-second time resolution, driven by a wide range of market participants and facilitated by "high-frequency" market makers [45]. The development of AI-based automated trading strategies for LOB markets has been a growth area in recent years, both within academia and industry, spurred on in part by developments in deep learning and reinforcement learning. Two typical LOB trading problems that have been investigated are market making, where the goal is to provide liquidity to the market by being continually willing to buy and sell an asset (see, e.g., Spooner et al. [50], Jerome et al. [28], Gasperov and Kostanjcar 1

Simulated environments are increasingly used by trading firms and investment banks to evaluate trading strategies before approaching real markets. Backtesting, a widely used approach, consists of simulating experimental strategies while replaying historical market scenarios. Unfortunately, this approach does not capture the market response to the experimental agents' actions. In contrast, multi-agent simulation presents a natural bottom-up approach to emulating agent interaction in financial markets. It allows to set up pools of traders with diverse strategies to mimic the financial market trader population, and test the performance of new experimental strategies. Since individual agent-level historical data is typically proprietary and not available for public use, it is difficult to calibrate multiple market agents to obtain the realism required for testing trading strategies. To addresses this challenge we propose a synthetic market generator based on Conditional Generative Adversarial Networks (CGANs) trained on real aggregate-level historical data. A CGAN-based "world" agent can generate meaningful orders in response to an experimental agent. We integrate our synthetic market generator into ABIDES, an open source simulator of financial markets. By means of extensive simulations we show that our proposal outperforms previous work in terms of stylized facts reflecting market responsiveness and realism.